Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction

We describe quantum circuits with only O ~ ( N ) Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of N arbitrary (e.g., molecular) orbitals. With O ( λ/ϵ ) repetitions of these circuits one can use phase estimation to sample in the molecular eigenbasis, w...

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Bibliographic Details
Published in:PRX quantum Vol. 2; no. 3; p. 030305
Main Authors: Lee, Joonho, Berry, Dominic W., Gidney, Craig, Huggins, William J., McClean, Jarrod R., Wiebe, Nathan, Babbush, Ryan
Format: Journal Article
Language:English
Published: United States American Physical Society (APS) 01.07.2021
American Physical Society
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
electronic structure
electronic structure calculations
quantum algorithms
quantum computation
quantum simulation
strongly correlated systems
ISSN:2691-3399, 2691-3399
Online Access:Get full text
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Summary:We describe quantum circuits with only O ~ ( N ) Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of N arbitrary (e.g., molecular) orbitals. With O ( λ/ϵ ) repetitions of these circuits one can use phase estimation to sample in the molecular eigenbasis, where λ is the 1-norm of Hamiltonian coefficients and ϵ is the target precision. This is the lowest complexity shown for quantum computations of chemistry within an arbitrary basis. Furthermore, up to logarithmic factors, this matches the scaling of the most efficient prior block encodings that can work only with orthogonal-basis functions diagonalizing the Coloumb operator (e.g., the plane-wave dual basis). Our key insight is to factorize the Hamiltonian using a method known as tensor hypercontraction (THC) and then to transform the Coulomb operator into an isospectral diagonal form with a nonorthogonal basis defined by the THC factors. We then use qubitization to simulate the nonorthogonal THC Hamiltonian, in a fashion that avoids most complications of the nonorthogonal basis. We also reanalyze and reduce the cost of several of the best prior algorithms for these simulations in order to facilitate a clear comparison to the present work. In addition to having lower asymptotic scaling space-time volume, compilation of our algorithm for challenging finite-sized molecules such as FeMoCo reveals that our method requires the least fault-tolerant resources of any known approach. By laying out and optimizing the surface-code resources required of our approach we show that FeMoCo can be simulated using about four million physical qubits and under 4 days of runtime, assuming 1- μ s cycle times and physical gate-error rates no worse than 0.1 % .
Bibliography:Australian Research Council (ARC)
USDOE Laboratory Directed Research and Development (LDRD) Program
PNNL-SA-157861
AC05-76RL01830; DP190102633; DP21010136; SC0012704
ISSN:2691-3399
2691-3399
DOI:10.1103/PRXQuantum.2.030305